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Concept
Rydberg formula
Summary
In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It was first empirically stated in 1888 by the Swedish physicist Johannes Rydberg, then theoretically by Niels Bohr in 1913, who used a primitive form of quantum mechanics. The formula directly generalizes the equations used to calculate the wavelengths of the hydrogen spectral series.
In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement. He plotted the wavenumbers (n) of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted.
First he tried the formula: , where n is the line's wavenumber, n0 is the series limit, m is the line's ordinal number in the series, m is a constant different for different series and C0 is a universal constant. This did not work very well.
Rydberg was trying: when he became aware of Balmer's formula for the hydrogen spectrum In this equation, m is an integer and h is a constant (not to be confused with the later Planck constant).
Rydberg therefore rewrote Balmer's formula in terms of wavenumbers, as .
This suggested that the Balmer formula for hydrogen might be a special case with and , where , the reciprocal of Balmer's constant (this constant h is written B''' in the Balmer equation article, again to avoid confusion with Planck's constant).
The term was found to be a universal constant common to all elements, equal to 4/h.
Official source
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